Billy, you said the park ranger said that Teel's Texas battery was assigned to the third brigade of McCown's division.

The records that I have seen certainly don't tell everything, but with all due respect to the park ranger, I’m rather certain that Teel’s Texas Btry did not serve in McCown’s or any other division of the Army of the West. As already stated, Teel’s Texas Btry was serving under Sibley in the New Mexico campaign in 1862

Tull’s Missouri Btry [as stated] was sometimes confused for Teel’s Texas Btry. But it merged with Bledsoe’s Company about April 21, 1862.

https://tshaonline.org/handbook/online/articles/qkt11
Teel's Texas Battery
…Although sources fail to agree, the battery seems to have consisted of two sections, those of first lieutenants Joseph H. McGinnis and Jordan W. Bennett, and each section was armed with two six-pounder guns. Teel was elected captain…
Near the end of the New Mexico campaign, sometime in the spring of 1862, Bennett replaced Teel (who had been promoted to major) as battery commander, and the unit was assigned to Earl Van Dorn's Army of the West. It seems, however, to have been disbanded shortly thereafter, for it did not serve at the September 19 battle of Iuka.
[Danny's note-I have extensive records on the Army of the West and have not yet found any reference to this battery being assigned to that army, either as Teel or Bennett]

Compiled service records for Teel’s Btry:
Organized 5/1/61 principally of former members of Capt Teel’s Co Tex State Troops and reorganized 11/22/63. Served for a time as Co B, 1st Regt CSA Artillery, Texas volunteers [unorganized] and as Co B Dege’s Bn light Arty.
Known at various times as Teel’s, Bennett’s and McMahan’s Co Tex Horse Arty but was finally designated as the 2nd Tex Field Btry and assigned to the 1st Bn field Arty by S O #290 Trans Miss Dept of 11/19/64

Compiled service Records for Lt Jordan Bennett:
2/2/62 Ref at Fort Thorn-requisition signed by Lt Bennett cdg Co B, Tex Arty, CSA Artillery

4/10/62 Ref at Santa Fe requisition signed by1st Lt Bennett Arty

9/22/62 San Antonio-officers of the 2nd Regt Tex Mtd Rifles requesting that Lt Bennett of Capt Teel’s light battery be authorized to raise the company for the 2nd Regt Tex Mtd Rifles…he has the company ready to muster in
Month of April 63 at Port Lavaca, Texas-Capt Bennett cdg

7/16/63 Ref at Indianola, Tex
Capt Bennett promoted from 1st Lt to Capt on 4/1/63 to rank from 2/21/62. Teel promoted Major 2/21/62.

12/22/63 Bennett’s Btry was broken up per S O #78 District of Tex, NM & Arizona. The enlisted men were assigned to duty under Capt McMahon